Strong Shift Equivalence of $C^{\ast }$-correspondences

Abstract

We define a notion of strong shift equivalence for $C^{\ast }$-correspondences and show that strong shift equivalent $C^{\ast }$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.

26 pages. Final version to appear in Israel Journal of Mathematics